The caution flag came out with defending Daytona 500 champion William Byron out front.
Rain started falling in turns one and two, the West side of the 2 1/2-mile Daytona International Speedway.
Trump spoke to the drivers as he led them through several ceremonial laps.
"This is your favorite president. I'm a big fan. I am a really big fan of you people," Trump said. "How you do this I don't know, but I just want you to be safe. You're talented people and you're great people and great Americans. Have a good day, have a lot of fun and I'll see you later."
NASCAR officials moved the start time to 2 p.m. Eastern earlier this week - 70 minutes ahead of the planned green flag - because of potential rain. Inclement weather is expected to be in the area between 4 p.m. and 5 p.m., with forecasts showing 99% chance of rain. And since it takes roughly two hours to dry the track, it could be 7 p.m. before the race resumes.
" Captain America " actor Anthony Mackie landed at the "Great American Race" and gave the command for drivers to start their engines.